Nucleus-nucleus scattering in the high-energy approximation and optical folding potential

Abstract

Nucleus-Nucleus Scattering in the High-Energy Approximation and the Optical Folding PotentialFor the nucleus-nucleus scattering, the complex potential is obtained which corresponds to the eikonal phase of an optical limit of the Glauber-Sitenko high-energy approximation. The potential does not include free parameters, its real and imaginary parts depend on energy and are determined by the reported data on the nuclear density distributions and nucleon-nucleon scattering amplitude. Alternatively, for the real part, the folding potential can be utilized which includes the effective NN -forces and the exchange term, as well. As a result, the microscopic optical potential is constructed where contributions of the calculated real and imaginary parts are formed by fitting the two respective factors. An efficient of the approach is confirmed by agreements of calculations with the experimental data on elastic scattering cross-sections.The investigation has been performed at the Bogoliubov Laboratory of Theoretical Physics, JINR. ‚´ ¸ÉµÖÐ¥°· ¡µÉ¥ ³Ò ¶·¥¤² £ ¥³ ³¨±·µ¸±µ ¶¨Î¥¸±¨° ¶µ¤Ìµ¤, £¤¥ ± ± ¢¥Ð¥¸É¢¥´´ Ö, É ±¨³´¨³ Ö Î ¸ÉÓ ¶µÉ¥´Í¨ ² ¢ÒΨ¸²ÖÕɸִ ¡ §¥ ³¨±·µ-±µ ¶¨Î¥¸±¨Ì ³µ¤¥²¥°. ' Ôɵ°Í¥²ÓÕ¨¸ ¶µ²Ó §Ê¥É¸Ö µ ¶É¨Î¥¸±¨° ¶µÉ¥´Í¨ ², ±µ-ɵ·Ò°³µ¦´µ´ °É¨± ± ɵδµ¥¸µµÉ¢¥É¸É¢¨¥ µ ¶É¨Î¥¸±µ³Ê ¶·¥¤¥²Ê ³¨±·µ¸±µ- ¶¨Î¥¸±µ°³µ¤¥²¨· ¸¸¥Ö´¨Ö ¢ ¢Ò¸µ±µÔ´¥·£¥É¨Î¥¸±µ³ ¶·¨¡²¨¦¥´¨¨(‚), ¶·¥¤²µ¦¥´´µ°¢´ Î ²¥ ƒ² Ê¡¥·µ³¨'¨É¥´±µ ¤²Ö ¤·µ´-Ö¤¥·´µ£µ · ¸¸¥Ö´¨Ö [10, 11], ¶µ §¤´¥¥ µ¡µ¡Ð¥´´µ°´ ¸²ÊÎ °· ¸¸¥Ö´¨Ö Ö¤¥· [12,13]. ‚ ·Ö¤¥ ²ÊÎ ¥¢ ¤²Ö · ¸Î¥É ¢¥Ð¥¸É¢¥´´µ°Î ¸É¨ ¶µÉ¥´Í¨ ² ³Ò¨¸ ¶µ²Ó §Ê¥³ É ±¦¥ OE""¸ÊΥɵ³ µ¡³¥´ ´Ê±²µ´ ³¨. ÉµÉ ³ É¥·¨ ²¨ §²µ¦¥´¢ · §¤. 1¨2. ‚ · §¤. 3 ¶·¨¢µ¤ÖÉ¸Ö · ¸Î¥ÉÒ É ±¨Ì ¶µÉ¥´Í¨ ²µ¢, ¶·¥¤² £ ¥É¸Ö ³µ¤¥²Ó ¶µ¤£µ´±¨, ±µ£¤ ¢ ·Ó¨·ÊÕÉ¸Ö ¤¢ ´µ·³¨·ÊÕÐ¨Ì ³´µ¦¨É¥²Ö, µ ¶·¥¤¥²ÖÕÐ¨Ì ¢±² ¤ ¢¥Ð¥-É¢¥´´µ°¨³´¨³µ°Î ¸É¨ ¶µÉ¥´Í¨ ² , ¤ ´µ¸· ¢´¥´¨¥¸Ô±¸ ¶¥·¨³¥´É ²Ó´Ò³¥ Î¥´¨Ö³¨Ê ¶·Ê£µ£µ · ¸¸¥Ö´¨Ö.

Microscopic study on proton elastic scattering of helium and lithium isotopes at energy range up to 160 MeV/nucleon.

“…On the other hand, the imaginary part of the OP is calculated within the high-energy approximation (HEA) was derived in Ref. [7] on the basis of the eikonal phase inherent in the optical limit of the Glauber theory. It is expressed as [5,7]:…”

“…where v is the velocity of the nucleon-nucleus relative motion, ρ(q) is the form factors corresponding to the point-like nucleon density distribution of the nucleus, and f NN (q) is the amplitude of the NN scattering which depends on the transfer momentum q and can be specified in the form of a Gaussian function [7,8]. The quantitiesσ NN is the averaged over the isospins total NN cross section.…”

“…[5,8] as functions of energies. The Green function Monte Carlo (GFMC) density [9,10] is used for the stable nuclei, 4 He and 6,7 Li and the large-scale shell model (LSSM) density [11] is used for 6,8 He and 9,11 Li exotic nuclei The volume integrals of the real and imaginary parts of the OP (J R and J I ), respectively, are expressed as [5] …”

“…In the present work, a microscopic analysis of the available proton elastic scattering data of these light nuclei, 4,6,8 He and 6,7,9,11 Li in the energy range below 160 MeV/nucleon is considered. The theoretical calculation is given in section 2, while the results of calculations are presented in section 3.…”

“…The proton elastic scattering data on 4,6,8 He and 6,7,9,11 Li nuclei at energies below 160 MeV/nucleon are analyzed using the optical model. The optical potential (OP) is taken microscopically, with few and limited fitting parameters, using the single folding model for the real part and high-energy approximation (HEA) for the imaginary one.…”